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mesh: from quadrilateral to triangular

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lc

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Feb 21, 2012, 5:57:02 PM2/21/12
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Any link on how to do the conversion?
thx

Hans-Bernhard Bröker

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Feb 21, 2012, 7:04:40 PM2/21/12
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On 21.02.2012 23:57, lc wrote:
> Any link on how to do the conversion?

Add diagonals.

lc

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Feb 21, 2012, 8:30:03 PM2/21/12
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yes, but which one? tip: convexity

BGB

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Feb 21, 2012, 9:27:33 PM2/21/12
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Quad: 0, 1, 2, 3

Triangle A: 0, 1, 2
Triangle B: 0, 2, 3

the pattern is trivially extended to break any convex polygon into
triangles.

Poly: 0, 1, 2, 3, 4, 5

Triangle A: 0, 1, 2
Triangle B: 0, 2, 3
Triangle C: 0, 3, 4
Triangle D: 0, 4, 5

lc

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Feb 22, 2012, 2:40:49 AM2/22/12
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Thanks for your reply, I must add that I have a parametric surface in
space, so the mesh's quadrilaterals are r(u_i,v_j), the surface is
smooth, but with nodes.

Hans-Bernhard Bröker

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Feb 22, 2012, 1:19:33 PM2/22/12
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At the level of detail your question provided: just pick one at random.

> tip: convexity

... has nothing to do with anything else you mentioned.

Nicolas Bonneel

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Feb 22, 2012, 2:56:40 PM2/22/12
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if you have a parametric surface, then you can compute the curvature
tensor, and use the one diagonal which is as close as possible to the
principal eigen vector of the tensor, so as to minimize distortion.

lc

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Feb 22, 2012, 6:55:50 PM2/22/12
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On 02/22/2012 08:56 PM, Nicolas Bonneel wrote:
> if you have a parametric surface, then you can compute the curvature
> tensor, and use the one diagonal which is as close as possible to the
> principal eigen vector of the tensor, so as to minimize distortion.
thanks
Analytically the formulae are too much complicated (Riemann theta
functions) so I'd approximate the curvature with the mesh;
is there any book/articles/survey ?
are 9 points enough?
and at the edge?
thanks for any advice

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